We use new kinematic data from the ultra-faint Milky Way satellite Segue 1 to model its dark matter distribution and derive upper limits on the dark matter annihilation cross-section. Using gamma-ray flux upper limits from the Fermi satellite and MAGIC, we determine cross-section exclusion regions for dark matter annihilation into a variety of different particles including charged leptons. We show that these exclusion regions are beginning to probe the regions of interest for a dark matter interpretation of the electron and positron fluxes from PAMELA, Fermi, and HESS, and that future observations of Segue 1 have strong prospects for testing such an interpretation. We additionally discuss prospects for detecting annihilation with neutrinos using the IceCube detector, finding that in an optimistic scenario a few neutrino events may be detected. Finally we use the kinematic data to model the Segue 1 dark matter velocity dispersion and constrain Sommerfeld enhanced models. Show Partial Abstract